A Conservative Crank-Nicolson Fourier Spectral Method for the Space Fractional Schrödinger Equation with Wave Operators | Zendy

Lei Zhang | Zendy; Rui Yang | Zendy; Li Zhang | Zendy; Lisha Wang | Zendy

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A Conservative Crank-Nicolson Fourier Spectral Method for the Space Fractional Schrödinger Equation with Wave Operators

Author(s) -

Lei Zhang,

Rui Yang,

Li Zhang,

Lisha Wang

Publication year - 2021

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.579

H-Index - 28

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2021/5137845

Subject(s) - mathematics , spectral method , fourier transform , collocation (remote sensing) , crank–nicolson method , galerkin method , fourier series , mathematical analysis , schrödinger equation , space (punctuation) , numerical analysis , physics , finite element method , computer science , machine learning , thermodynamics , operating system

In this paper, the Crank-Nicolson Fourier spectral method is proposed for solving the space fractional Schrödinger equation with wave operators. The equation is treated with the conserved Crank-Nicolson Fourier Galerkin method and the conserved Crank-Nicolson Fourier collocation method, respectively. In addition, the ability of the constructed numerical method to maintain the conservation of mass and energy is studied in detail. Meanwhile, the convergence with spectral accuracy in space and second-order accuracy in time is verified for both Galerkin and collocation approximations. Finally, the numerical experiments verify the properties of the conservative difference scheme and demonstrate the correctness of theoretical results.

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